There are many variations of the Primacy of Consciousness. One view would hold that your mind is the only mind that exists, and everyone else is a product of your imagination. That’s a bit of a god-complex. Another view is that many minds exist, but we’re ultimately unconnected to them since there is no reality. Still another view is that there are multiple minds, and that reality is a kind of group average of them. Each person has their own idea of what reality should be, and somehow they’re all resolved in a common hallucination. You could spend hours coming up with other interesting and entirely useless alternatives.
The Primacy of Existence acts to remind us that the world is out there, and we have to act accordingly. In epistemology, it means that we have to look to reality to understand it. If we’re mistaken about the nature of reality, then our actions won’t work. Reality exists in a particular way, and if we don’t grasp it, we lose. In ethics, it highlights the fact that you can’t just wish for something, and you have to follow facts in order to get a desired result. If you act inappropriately, you will suffer. If you grasp reality and act properly, you’ll live the good life. Some methods and actions are better than others when trying to achieve a goal. Some are just wrong, and cannot produce it.
So there’s a “real world” out there, outside your brain; and then there’s the “virtual world” that has been built inside your brain. The real and the virtual world never match up completely, but they can correspond to a greater or lesser degree. When you see a blue ball, you can be pretty confident that there really is a ball and it really has the property of being blue. The color blue is not really a “thing”; it is just a word that we use to label light at a certain wavelength. But there really is light, and it really has different wavelengths, and it really does bounce off of things like balls to show you the color blue.
When we talk about “objective reality”, we are talking about the world that’s really there, unfiltered, outside your mind. Our beliefs do not change the world, except to the extent that they lead to actions that alter reality. So I can, if I try hard enough, go around all day sincerely believing things like “That blue ball is actually an orange artichoke” or “There’s an invisible man living in the sky who watches everything you do, every minute of every day” or “The British government has learned that Saddam Hussein recently sought significant quantities of uranium from Africa.” But if those things are not correct statements about the real world, then no amount of belief will change that.